By Le Chatelier's principle, increasing the concentration of a weak electrolyte brings out more ions.

By Ostwald's dilution law, increasing the concentration of a weak electrolyte brings out less ions ($a = \sqrt{K_\mathrm{a}/C}$).

Where do we stand?

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    $\begingroup$ Le Chatelier pr is about keeping equilibrium Ostwald l. is about defining which value is equilibrium. $\endgroup$ – Alchimista Dec 27 '18 at 12:24
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    $\begingroup$ You interpret Ostwald's law wrong. Increasing the concentration of a weak electrolyte would produce more ions, just not as much more as it would in the case of strong electrolyte. $\endgroup$ – Ivan Neretin Dec 27 '18 at 13:47

Le Chatelier's Principle makes no quantitative predictions. In this case, all it says is that adding, let us say, more acetic acid to an aqueous acetic acid solution will give more solvated protons and acetate ions in solution. But it does not guarantee that the amount of additional ions varies in direct proportion to the acetic acid concentration. We need such a proportional variation to maintain the same value of $a$ in the Ostwald equation, but Le Chatelier's Principle allows the possibility that maybe the increase is not enough to match the proportional variation. If we suppose that the amount of ions increases only with the square root of added solute, and work out the fractional ionization $a$ from that assumption we get exactly the Ostwald relation.

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